<p>Parity checkers are widely used in digital systems to detect errors when systems are in operation. Since parity checkers are monitoring circuits, their reliability must be guaranteed by performing a thorough testing. In this work, multiple fault detection of parity checkers is investigated. We have found that all multiple stuck-at faults occurring on a parity tree can be completely detected using test patterns provided by the identity matrix plus zero vector. The identity matrix contains 1's on the main diagonal and 0's elsewhere; while the zero vector contains 0's. The identity matrix vectors can also detect all multiple general bridging faults, if the bridgings result in a wired-AND effect. However, test patterns generated from the identity matrix and binary matrix are required to detect a majority of the multiple bridging faults which yield wired-OR connections. Note that the binary matrix contains two 1's at each column of the matrix.</p>